Great write-up. Inspired me to try how much further ICL could go beyond "simpler" mappings (OP shows pretty nice results for two linear and two quadratic functions). As such, I tried a damped sinusoid:

with the prompt:

x=3.984, y=6.68 x=2.197, y-2.497 x=0.26, y=-7.561 x=6.025, y=-1.98 x=7.126, y=-4.879 x=8.584, y=-0.894 x=9.97, y=3.403 x=11.1, y=2.45 x=12.09, y=-0.452 x=13.72, y=-2.48 x=14.81, y=-0.606 x=10, y=

but didn't get any luck. Maybe I need more points, especially around the troughs and valleys.

Great write-up. Inspired me to try how much further ICL could go beyond "simpler" mappings (OP shows pretty nice results for two linear and two quadratic functions). As such, I tried a damped sinusoid:

with the prompt:

but didn't get any luck. Maybe I need more points, especially around the troughs and valleys.